We introduce an exact, two-parameter family of static, spherically-symmetric, constant-curvature $Λ$-vacuum solutions within the four-dimensional Starobinsky $f(R)=R+αR^2+2Λ$ model. When the bare cosmological constant is precisely fine-tuned to $Λ= 1/(8α)$, the scalar curvature is rigidly fixed such that the derivative $f'(R)=1+2αR$ identically vanishes. Because this derivative acts as the effective multiplier for the standard curvature terms in the modified field equations, its global vanishing mathematically erases the normal rules of gravitational dynamics, demonstrating that the family represents a pathological boundary to the space of viable physical geometries. This exact decoupling of the field equations permits the existence of a fundamentally unconstrained $1/r^2$ integration constant in the metric, which functions as a purely geometric Reissner-Nordstrom hair mimicker. However, any infinitesimal classical deviation from this exact boundary instantaneously destroys the degeneracy, rigorously forcing the geometric hair to vanish and discontinuously collapsing the spacetime back into the standard, dynamical Schwarzschild-de Sitter solution. We provide the exact derivation of this spacetime and methodically highlight its physical pathologies, including the identically vanishing Wald entropy of the associated black hole horizons, the strict divergence of the effective gravitational coupling, the complete breakdown of the test-particle approximation, and the onset of severe ghost instabilities. Ultimately, this exact solution functions as a ``do not enter'' sign within the Starobinsky model, pedagogically illustrating the extreme fragility and physical hostility of degenerate, purely mathematical solutions in highly non-linear $f(R)$ gravity theories.
We investigate the problem of static and spherically symmetric solutions in the Starobinsky gravity model. By extending the Lichnerowicz and Israel theorems, William Nelson have demonstrated that the Schwarzschild solution is the unique static, spherically symmetric, and asymptotically flat black hole solution in the Starobinsky model. However, Hong L{ü} et al find that there are sign errors in the proof of Nelson. This raises the problem whether Nelson's proof is correct or not. In order to answer this question, we explore the corresponding solutions by using the Taylor series expansion metho…
The vacuum solutions around a spherically symmetric and static object in the Starobinsky model are studied with a perturbative approach. The differential equations for the components of the metric and the Ricci scalar are obtained and solved by using the method of matched asymptotic expansions. The presence of higher order terms in this gravity model leads to the formation of a boundary layer near the surface of the star allowing the accommodation of the extra boundary conditions on the Ricci scalar. Accordingly, the metric can be different from the Schwarzschild solution near the star dependi…
In this work, we explore wormhole solutions in $f(R,T)$ theory of gravity, where $R$ is the scalar curvature and $T$ is the trace of stress-energy tensor of matter. To investigate this, we consider static spherically symmetric geometry with matter contents as anisotropic, isotropic and barotropic fluids in three separate cases. By taking into account Starobinsky $f(R)$ model , we analyze the behavior of energy conditions for these different kind of fluids. It is shown that the wormhole solutions can be constructed without exotic matter in few regions of spacetime. We also give the graphical il…
The existence of black holes is one of the key predictions of general relativity (GR) and therefore a basic consistency test for modified theories of gravity. In the case of spherical symmetry in GR the existence of an apparent horizon and its regularity is consistent with only two distinct classes of physical black holes. Here we derive constraints that any self-consistent modified theory of gravity must satisfy to be compatible with their existence. We analyze their properties and illustrate characteristic features using the Starobinsky model. Both of the GR solutions can be regarded as zero…
Circular stable orbits in $f(R)$ realistic static and spherically-symmetric spacetimes
Universidad Complutense de Madrid（马德里康普顿斯大学）；Universidad de Salamanca（萨拉曼卡大学）；University of Cape Town（开普敦大学）；Instituto de Física Corpuscular (IFIC), CSIC‐Universitat de València（瓦伦西亚大学与西班牙国家研究委员会联合粒子物理研究所）；Universidade Federal do Ceará（塞阿拉联邦大学）
This paper is devoted to studying charged anisotropic static spherically symmetric solutions through gravitationally decoupled minimal geometric deformation technique in $f(R)$ gravity. For this purpose, we first consider the known isotropic Krori-Barua solution for $f(R)$ Starobinsky model in the interior of a charged stellar system and then include the effects of two types of anisotropic solutions. The corresponding field equations are constructed and the unknown constants are obtained from junction conditions. We analyze the physical viability and stability of the resulting solutions throug…
C-infinity Compact-Support Wormholes with Exact Schwarzschild Exterior in Trace-Coupled Gravity
National University of Computer and Emerging Sciences（国立计算机与新兴科学大学）；Center for Theoretical Physics, Khazar University（哈扎尔大学理论物理中心）；School of Computing and Mathematical Sciences, University of Leicester（莱斯特大学计算与数学科学学院）；Department of Physics, College of Sciences, Princess Nourah bint Abdulrahman University（公主努拉·宾特·阿卜杜勒拉赫曼大学理学院物理学系）
